活动类型: | 学术活动 |
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活动名称: | Long-time asymptotics of the Sawada-Kotera equation and Kaup-Kupershmidt equation on the line |
地点: | 中关村教学楼第二层 N210 |
主讲人: | 王东 |
联系人: | 王东 |
联系方式: | 15910781583 |
开始时间: | 2023-12-18 15:00 |
结束时间: | 2023-12-18 17:00 |
说明: |
SourceURL:file:///home/wangd-math/Downloads/王灯山-报告相关信息.docx In this talk, we report our recent studies on the long-time asymptotics of the Sawada-Kotera (SK) equation and Kaup-Kupershmidt (KK) equation. Both SK equation and KK equation are integrable systems with third-order Lax operator. Moreover, they are related with the same modified nonlinear equation (called modified SK-KK equation) by Miura transformations. This work first constructs the Riemann-Hilbert problem associated with the SK equation, KK equation and modified SK-KK equation by direct and inverse scattering transforms. Then the long-time asymptotics of these equations are studied based on Deift-Zhou steepest-descent method for Riemann-Hilbert problem. Finally, it is shown that the asymptotic solutions match very well with the results of direct numerical simulations. This is a joint work with Xiaodong Zhu. |